Recall that $\sin^{-1}$ is the inverse function of $\sin$, as defined in the standard fashion. (Sometimes $\sin^{-1}$ is called $\arcsin$.) Let $f(x) = \sin^{-1}(\sin(\pi x))$. Write the values of the following. (Some answers may involve the irrational number $\pi$. Write such answers in terms of $\pi$.)\\
(i) $f(2.7)$\\
(ii) $f'(2.7)$\\
(iii) $\int_0^{2.5} f(x)\, dx$\\
(iv) the smallest positive $x$ at which $f'(x)$ does not exist.